I think it's more likely that Cashman gets fired if the Yankees miss the playoffs than he resigns to run for Governor of Connecticut.
As for running for elected office, Connecticut is part of Red Sox Nation. Cashman wouldn't win there, no matter party he affiliated with.
He'd be better off carpetbagging across the New York State line and trying to run against Cuomo.
He could move to Westchester or Putnam....could he win against Cuomo?
He is a friend of Brett Kavanaugh and Neil Gorsuch....
He might win a Democratic Primary and leave Cuomo with the Working Families line if he chose to run as a Democrat. But if he chose to run as a Republican, he'd have no chance.